A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems

Autores
Angiono, Iván Ezequiel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
Fil: Angiono, Iván Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/53098
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/53098
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systemsAngiono, Iván EzequielNichols AlgebrasPointed Hopf AlgebrasQuantized Enveloping Algebrashttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.Fil: Angiono, Iván Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaEuropean Mathematical Society2015-10-29info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/53098Angiono, Iván Ezequiel; A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems; European Mathematical Society; Journal of the European Mathematical Society; 17; 10; 29-10-2015; 2643-26711435-9855CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=17&iss=10&rank=7info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/567info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:51:22Zoai:ri.conicet.gov.ar:11336/53098instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:51:22.385CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
spellingShingle A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
Angiono, Iván Ezequiel
Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
title_short A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_full A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_fullStr A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_full_unstemmed A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
title_sort A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems
dc.creator.none.fl_str_mv Angiono, Iván Ezequiel
author Angiono, Iván Ezequiel
author_facet Angiono, Iván Ezequiel
author_role author
dc.subject.none.fl_str_mv Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
topic Nichols Algebras
Pointed Hopf Algebras
Quantized Enveloping Algebras
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
Fil: Angiono, Iván Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based on Kharchenko's theory of PBW bases of Lyndon words. We prove that the lexicographic order on Lyndon words is convex for PBW generators and so the PBW basis is orthogonal with respect to the canonical non-degenerate form associated to the Nichols algebra.
publishDate 2015
dc.date.none.fl_str_mv 2015-10-29
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/53098
Angiono, Iván Ezequiel; A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems; European Mathematical Society; Journal of the European Mathematical Society; 17; 10; 29-10-2015; 2643-2671
1435-9855
CONICET Digital
CONICET
url http://hdl.handle.net/11336/53098
identifier_str_mv Angiono, Iván Ezequiel; A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems; European Mathematical Society; Journal of the European Mathematical Society; 17; 10; 29-10-2015; 2643-2671
1435-9855
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.ems-ph.org/journals/show_abstract.php?issn=1435-9855&vol=17&iss=10&rank=7
info:eu-repo/semantics/altIdentifier/doi/10.4171/JEMS/567
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society
publisher.none.fl_str_mv European Mathematical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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